Constructing 8 × 8 S-Boxes with Optimal Boolean Function Nonlinearity

Abstract: Substitution boxes (S-Boxes) are the core components of modern block ciphers, responsible for introducing the essential nonlinearity that protects against attacks like linear and differential cryptanalysis. For an 8-bit S-Box, the highest possible nonlinearity for a balanced Boolean function is 116. The best results previously reported in the literature achieved an average nonlinearity of 114.5 across the coordinate Boolean functions of 8 × 8 S-boxes. Our proposed method surpasses this record, producing S-boxes whose coordinate functions exhibit an average nonlinearity of 116. This is a significant achievement as it reaches the best result to date for the nonlinearity of the coordinate Boolean functions of an S-Box. Our S-Box generation method is based on multiplication over the field GF(24) and 4×4 component S-Boxes. The approach is also highly effective, capable of producing a large number of S-Boxes with good cryptographic properties. Other cryptographic criteria, such as BIC, SAC, DAP, and LAP, though not fully optimal, remain within acceptable ranges when compared with other reported designs. In addition, a side-channel attack evaluation is presented, covering both parameter analysis and experimental results on a real system when applying the proposed S-Box in the AES algorithm. These results make it a leading solution for block cipher design.